In multi-stage jobs, each
job consists of multiple coflows and is represented by a Directed
Acyclic Graph (DAG). Compared with the most common GNN architecture
that aggregates information from neighbouring nodes at the previous
layer based on message passing, DAGNN is driven by the partial order
induced by the DAG and aggregates neighbourhood information in the
current layer [1]}. Note that DAGNN exploits an inductive
bias that relies on the assumption that the input graph is a DAG.
To facilitate subsequent understanding, we first briefly describe
the DAGNN framework:
\(\begin{aligned}H_{v}^{\ell }=F^{\ell }\left(G^{\ell }\left(\left\lbrace  H_{u}^{\ell }\mid u\in \mathcal {P}(v)\right\rbrace  ,H_{v}^{\ell -1}\right),H_{v}^{\ell -1}\right),\\\ell =1,\ldots ,L\end{aligned}\) 
\(H_{\mathcal {G}}=R\left(\left\lbrace  H_{v}^{\ell },\ell =0,1,\ldots ,L,v\in \mathcal {T}\right\rbrace  \right)\) 
